5.348. size_max_starting_seq_alldifferent
| DESCRIPTION | LINKS | GRAPH |
- Origin
- Constraint
- Synonyms
, , .
- Arguments
- Restrictions
- Purpose
is the size of the maximal sequence (among all sequences of consecutive variables of the collection starting at position one) for which the constraint holds.
- Example
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The first constraint holds since the constraint holds and since does not hold.
- Typical
- Symmetry
One and the same constant can be added to the attribute of all items of .
- Arg. properties
Functional dependency: determined by .
- Remark
A conditional constraintΒ [MittalFalkenhainer90] with the specific structure that one can relax the constraints on the last variables of the collection .
- Counting
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Length () 2 3 4 5 6 7 8 Solutions 9 64 625 7776 117649 2097152 43046721 Number of solutions for : domains
Length () 2 3 4 5 6 7 8 Total 9 64 625 7776 117649 2097152 43046721 Parameter value 1 3 16 125 1296 16807 262144 4782969 2 6 24 200 2160 28812 458752 8503056 3 - 24 180 2160 30870 516096 9920232 4 - - 120 1440 23520 430080 8817984 5 - - - 720 12600 268800 6123600 6 - - - - 5040 120960 3265920 7 - - - - - 40320 1270080 8 - - - - - - 362880 Solution count for : domains
- See also
common keyword: , , Β (all different,disequality).
implies: .
- Keywords
characteristic of a constraint: all different, disequality, hypergraph.
combinatorial object: sequence.
constraint arguments: pure functional dependency.
constraint type: sliding sequence constraint, open constraint, conditional constraint.
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Note that this is an example where the arc constraints do not have the same arity. However they correspond to the same constraint.
PartsΒ (A) andΒ (B) of FigureΒ 5.348.1 respectively show the initial and final graph associated with the first example of the Example slot.
Figure 5.348.1. (A)Β Initial and (B)Β final graph of the constraint of the first example of the Example slot where each ellipse represents an hyperedge corresponding to an constraint (e.g., the fourth ellipse represents the constraint )
